Relaxation under outflow dynamics with random sequential updating

TL;DR

This paper compares relaxation dynamics in various Sznajd model variants with random sequential updating on chains and square lattices, highlighting differences in relaxation speed and behavior.

Contribution

It provides a comparative analysis of different Sznajd model versions and their relaxation properties using Monte Carlo simulations and mean field approaches.

Findings

Galam rule relaxes faster than Stauffer rule.

No qualitative differences between the two generalizations on the square lattice.

Monte Carlo and mean field results show consistent relaxation patterns.

Abstract

In this paper we compare the relaxation in several versions of the Sznajd model (SM) with random sequential updating on the chain and square lattice. We start by reviewing briefly all proposed one dimensional versions of SM. Next, we compare the results obtained from Monte Carlo simulations with the mean field results obtained by Slanina and Lavicka . Finally, we investigate the relaxation on the square lattice and compare two generalizations of SM, one suggested by Stauffer and another by Galam. We show that there are no qualitative differences between these two approaches, although the relaxation within the Galam rule is faster than within the well known Stauffer rule.